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dc.contributor.advisorXu, Dr. Hongguo
dc.contributor.authorSaraswat, Jyoti
dc.date.accessioned2009-10-13T04:25:22Z
dc.date.available2009-10-13T04:25:22Z
dc.date.issued2009-06-11
dc.date.submitted2009
dc.identifier.otherhttp://dissertations.umi.com/ku:10431
dc.identifier.urihttp://hdl.handle.net/1808/5528
dc.description.abstractThe study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices. The connection provides a different angle to view the Vandermonde-like systems. Krylov subspace methods are strongly related to polynomial spaces, hence a nice connection can be established using LU factorization as proposed by Bjorck and Pereyra and QR factorization by Reichel. Further an algorithm to generate a preconditioner is incorporated in GR algorithm given by Reichel . This generates a preconditioner for Vandermonde-like matrices consisting of polynomials which obey a three term recurrence relation. This general preconditioner works effectively for Vandermonde matrices as well. The preconditioner is then tested on various distinct nodes. Based on results obtained, it is established that the condition number of Vandermonde -like matrices can be lowered significantly by application of the preconditioner, for some cases.
dc.format.extent88 pages
dc.language.isoEN
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.subjectKrylov matrix
dc.subjectPreconditioner
dc.subjectVandermonde matrix
dc.titleA Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.
dc.typeThesis
dc.contributor.cmtememberHuang, Weizhang
dc.contributor.cmtememberVleck, Dr. Erik Van
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelM.A.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
kusw.bibid7079062
dc.rights.accessrightsopenAccess


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